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Gravitational instantons and fluxes from M/F-theory on Calabi-Yau fourfolds

Thomas W. Grimm* and Raffaele Savelli†

  • Max-Planck-Institut für Physik, Föhringer Ring 6, 80805 Munich, Germany

  • *grimm@mpp.mpg.de
  • †savelli@mpp.mpg.de
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Phys. Rev. D 85, 026003 – Published 13 January, 2012

DOI: https://doi.org/10.1103/PhysRevD.85.026003

Abstract

We compactify four-dimensional N=1 gauged supergravity theories on a circle including fluxes for shift-symmetric scalars. Four-dimensional Taub-NUT gravitational instantons universally correct the three-dimensional superpotential in the absence of fluxes. In the presence of fluxes these Taub-NUT instanton contributions are no longer gauge-invariant. Invariance can be restored by gauge-instantons on top of Taub-NUT instantons. We establish the embedding of this scenario into M-theory. Circle fluxes and gaugings arise from a restricted class of M-theory four-form fluxes on a resolved Calabi-Yau fourfold. The M5-brane on the base of the elliptic fourfold dualizes into the universal Taub-NUT instanton. In the presence of fluxes this M5-brane is anomalous. We argue that anomaly-free contributions arise from involved M5-brane geometries dual to gauge-instantons on top of Taub-NUT instantons. Adding a four-dimensional superpotential to the gravitational instanton corrections leads to three-dimensional Anti-de Sitter vacua at stabilized compactification radius. We comment on the possibility to uplift these M-theory vacua, and to tunnel to four-dimensional F-theory vacua.

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Phys. Rev. D 85, 026003– Published 13 January, 2012
  • Received 18 October 2011

© 2012 American Physical Society

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